Isn't s and t switched in the image? If i is the x coordinate s should be horizontal right?

I think if we interpolate vertically first, we would get the exact same result.

Vertically interpolating will only change the order of the operation, but in such a way that it doesn't change the actual output.

Does this mean that we sample at the corners of the pixels?

I think the order of interpolation doesn't matter.

If the vertical pixels are blended first, the final result should be the same.

The final result would remain the same.